Among all the occurrences possible in the universe the a priori probability of any particular one of them verges upon zero. Yet the universe exists; particular events must take place in it, the probability of which (before the event) was infinitesimal. At the present time we have no legitimate grounds for either asserting or denying that life got off to but a single start on earth, and that, as a consequence, before it appeared its chances of occurring were next to nil. ... Destiny is written concurrently with the event, not prior to it.

An evolution is a series of events that in itself as series is purely physical, — a set of necessary occurrences in the world of space and time. An egg develops into a chick; … a planet condenses from the fluid state, and develops the life that for millions of years makes it so wondrous a place. Look upon all these things descriptively, and you shall see nothing but matter moving instant after instant, each instant containing in its full description the necessity of passing over into the next. … But look at the whole appreciatively, historically, synthetically, as a musician listens to a symphony, as a spectator watches a drama. Now you shall seem to have seen, in phenomenal form, a story.

As soon as the circumstances of an experiment are well known, we stop gathering statistics. … The effect will occur always without exception, because the cause of the phenomena is accurately defined. Only when a phenomenon includes conditions as yet undefined,Only when a phenomenon includes conditions as yet undefined, can we compile statistics. … we must learn therefore that we compile statistics only when we cannot possibly help it; for in my opinion, statistics can never yield scientific truth.

Events and developments, such as … the Copernican Revolution, … occurred only because some thinkers either decided not to be bound by certain “obvious” methodological rules, or because they unwittingly broke them.

Every occurrence in Nature is preceded by other occurrences which are its causes, and succeeded by others which are its effects. The human mind is not satisfied with observing and studying any natural occurrence alone, but takes pleasure in connecting every natural fact with what has gone before it, and with what is to come after it.

How strange it would be if the final theory were to be discovered in our lifetimes! The discovery of the final laws of nature will mark a discontinuity in human intellectual history, the sharpest that has occurred since the beginning of modern science in the seventeenth century. Can we now imagine what that would be like?

I was sitting in a chair in the patent office at Bern when all of a sudden a thought occurred to me: “If a person falls freely he will not feel his own weight.” I was startled. This simple thought made a deep impression on me. It impelled me toward a theory of gravitation.

Lecture in Japan (1922). The quote is footnoted in Michael White, John Gribbin, Einstein: a Life in Science (1995), 128, saying the talk is known as the 'Kyoto address', reported in J. Ishiwara, Einstein Koen-Roku (1977).

I would like to start by emphasizing the importance of surfaces. It is at a surface where many of our most interesting and useful phenomena occur. We live for example on the surface of a planet. It is at a surface where the catalysis of chemical reactions occur. It is essentially at a surface of a plant that sunlight is converted to a sugar. In electronics, most if not all active circuit elements involve non-equilibrium phenomena occurring at surfaces. Much of biology is concerned with reactions at a surface.

It is usual to say that the two sources of experience are Observation and Experiment. When we merely note and record the phenomena which occur around us in the ordinary course of nature we are said to observe. When we change the course of nature by the intervention of our will and muscular powers, and thus produce unusual combinations and conditions of phenomena, we are said to experiment. [Sir John] Herschel has justly remarked that we might properly call these two modes of experience passive and active observation. In both cases we must certainly employ our senses to observe, and an experiment differs from a mere observation in the fact that we more or less influence the character of the events which we observe. Experiment is thus observation plus alteration of conditions.

It was Darwin’s chief contribution, not only to Biology but to the whole of natural science, to have brought to light a process by which contingencies a priori improbable are given, in the process of time, an increasing probability, until it is their non-occurrence, rather than their occurrence, which becomes highly improbable.

From essay 'Retrospect of the Criticisms of the Theory of Natural Selection', reproduced in Julian Huxley, A.C. Hardy, and E.B. Ford (eds.), Evolution as a Process (1954), 91, as cited in Elizabeth Knowles, What They Didn't Say: A Book of Misquotations (2006), 79-80. “Natural selection is a mechanism for generating an exceedingly high degree of improbability,” which is seen more often, is a summary form of Fisher’s idea (not a verbatim quote) written by Julian Huxley, ibid, 5.

Life arose as a living molecule or protogene, the progression from this stage to that of the ameba is at least as great as from ameba to man. All the essential problems of living organisms are already solved in the one-celled (or, as many now prefer to say, noncellular) protozoan and these are only elaborated in man or the other multicellular animals. The step from nonlife to life may not have been so complex, after all, and that from cell to multicellular organism is readily comprehensible. The change from protogene to protozoan was probably the most complex that has occurred in evolution, and it may well have taken as long as the change from protozoan to man.

Nobody, certainly, will deny that the idea of the existence of an omnipotent, just, and omnibeneficent personal God is able to accord man solace, help, and guidance; also, by virtue of its simplicity it is accessible to the most undeveloped mind. But, on the other hand, there are decisive weaknesses attached to this idea in its elf, which have been painfully felt since the beginning of history. That is, if this being is omnipotent, then every occurrence, including every human action, every human thought, and every human feeling and aspiration is also His work; how is it possible to think of holding men responsible for their deeds and thoughts before such an almighty Being? In giving out punishment and rewards He would to a certain extent be passing judgment on Himself. How can this be combined with the goodness and righteousness ascribed to Him?

One of the main purposes of scientific inference is to justify beliefs which we entertain already; but as a rule they are justified with a difference. Our pre-scientific general beliefs are hardly ever without exceptions; in science, a law with exceptions can only be tolerated as a makeshift. Scientific laws, when we have reason to think them accurate, are different in form from the common-sense rules which have exceptions: they are always, at least in physics, either differential equations, or statistical averages. It might be thought that a statistical average is not very different from a rule with exceptions, but this would be a mistake. Statistics, ideally, are accurate laws about large groups; they differ from other laws only in being about groups, not about individuals. Statistical laws are inferred by induction from particular statistics, just as other laws are inferred from particular single occurrences.

Physicists often quote from T. H. White’s epic novel The Once and Future King, where a society of ants declares, “Everything not forbidden is compulsory.” In other words, if there isn't a basic principle of physics forbidding time travel, then time travel is necessarily a physical possibility. (The reason for this is the uncertainty principle. Unless something is forbidden, quantum effects and fluctuations will eventually make it possible if we wait long enough. Thus, unless there is a law forbidding it, it will eventually occur.)

Round about the accredited and orderly facts of every science there ever floats a sort of dust-cloud of exceptional observations, of occurrences minute and irregular and seldom met with, which it always proves more easy to ignore than to attend to … Anyone will renovate his science who will steadily look after the irregular phenomena, and when science is renewed, its new formulas often have more of the voice of the exceptions in them than of what were supposed to be the rules.

Scientific development depends in part on a process of non-incremental or revolutionary change. Some revolutions are large, like those associated with the names of Copernicus, Newton, or Darwin, but most are much smaller, like the discovery of oxygen or the planet Uranus. The usual prelude to changes of this sort is, I believed, the awareness of anomaly, of an occurrence or set of occurrences that does not fit existing ways of ordering phenomena. The changes that result therefore require 'putting on a different kind of thinking-cap', one that renders the anomalous lawlike but that, in the process, also transforms the order exhibited by some other phenomena, previously unproblematic.

Several very eminent living paleontologists frequently emphasise the abruptness of some of the major changes that have occurred, and seek for an external cause. This is a heady wine and has intoxicated palaeontologists since the days when they could blame it all on Noah's flood. In fact, books are still being published by the lunatic fringe with the same explanation. In case this book should be read by some fundamentalist searching for straws to prop up his prejudices, let me state categorically that all my experience (such as it is) has led me to an unqualified acceptance of evolution by natural selection as a sufficient explanation for what I have seen in the fossil record

The central problem of biological evolution is the nature of mutation, but hitherto the occurrence of this has been wholly refractory and impossible to influence by artificial means, although a control of it might obviously place the process of evolution in our hands.

The hypotheses which we accept ought to explain phenomena which we have observed. But they ought to do more than this; our hypotheses ought to foretell phenomena which have not yet been observed; ... because if the rule prevails, it includes all cases; and will determine them all, if we can only calculate its real consequences. Hence it will predict the results of new combinations, as well as explain the appearances which have occurred in old ones. And that it does this with certainty and correctness, is one mode in which the hypothesis is to be verified as right and useful.

The progress of synthesis, or the building up of natural materials from their constituent elements, proceeds apace. Even some of the simpler albuminoids, a class of substances of great importance in the life process, have recently been artificially prepared. ... Innumerable entirely new compounds have been produced in the last century. The artificial dye-stuffs, prepared from materials occurring in coal-tar, make the natural colours blush. Saccharin, which is hundreds of times sweeter than sugar, is a purely artificial substance. New explosives, drugs, alloys, photographic substances, essences, scents, solvents, and detergents are being poured out in a continuous stream.

The starting point of Darwin’s theory of evolution is precisely the existence of those differences between individual members of a race or species which morphologists for the most part rightly neglect. The first condition necessary, in order that any process of Natural Selection may begin among a race, or species, is the existence of differences among its members; and the first step in an enquiry into the possible effect of a selective process upon any character of a race must be an estimate of the frequency with which individuals, exhibiting any given degree of abnormality with respect to that, character, occur. The unit, with which such an enquiry must deal, is not an individual but a race, or a statistically representative sample of a race; and the result must take the form of a numerical statement, showing the relative frequency with which the various kinds of individuals composing the race occur.

The traditional mathematics professor of the popular legend is absentminded. He usually appears in public with a lost umbrella in each hand. He prefers to face a blackboard and to turn his back on the class. He writes a, he says b, he means c, but it should be d. Some of his sayings are handed down from generation to generation:“In order to solve this differential equation you look at it till a solution occurs to you.”“This principle is so perfectly general that no particular application of it is possible.”“Geometry is the science of correct reasoning on incorrect figures.”“My method to overcome a difficulty is to go round it.”“What is the difference between method and device? A method is a device which you used twice.”

The unprecedented identification of the spectrum of an apparently stellar object in terms of a large red-shift suggests either of the two following explanations.The stellar object is a star with a large gravitational red-shift. Its radius would then be of the order of 10km. Preliminary considerations show that it would be extremely difficult, if not impossible, to account for the occurrence of permitted lines and a forbidden line with the same red-shift, and with widths of only 1 or 2 per cent of the wavelength.The stellar object is the nuclear region of a galaxy with a cosmological red-shift of 0.158, corresponding to an apparent velocity of 47,400 km/sec. The distance would be around 500 megaparsecs, and the diameter of the nuclear region would have to be less than 1 kiloparsec. This nuclear region would be about 100 times brighter optically than the luminous galaxies which have been identified with radio sources thus far. If the optical jet and component A of the radio source are associated with the galaxy, they would be at a distance of 50 kiloparsecs implying a time-scale in excess of 105 years. The total energy radiated in the optical range at constant luminosity would be of the order of 1059 ergs.Only the detection of irrefutable proper motion or parallax would definitively establish 3C 273 as an object within our Galaxy. At the present time, however, the explanation in terms of an extragalactic origin seems more direct and less objectionable.

The wintry clouds drop spangles on the mountains. If the thing occurred once in a century historians would chronicle and poets would sing of the event; but Nature, prodigal of beauty, rains down her hexagonal ice-stars year by year, forming layers yards in thickness. The summer sun thaws and partially consolidates the mass. Each winter's fall is covered by that of the ensuing one, and thus the snow layer of each year has to sustain an annually augmented weight. It is more and more compacted by the pressure, and ends by being converted into the ice of a true glacier, which stretches its frozen tongue far down beyond the limits of perpetual snow. The glaciers move, and through valleys they move like rivers.

[In the case of research director, Willis R. Whitney, whose style was to give talented investigators as much freedom as possible, you may define “serendipity” as] the art of profiting from unexpected occurrences. When you do things in that way you get unexpected results. Then you do something else and you get unexpected results in another line, and you do that on a third line and then all of a sudden you see that one of these lines has something to do with the other. Then you make a discovery that you never could have made by going on a direct road.

In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) -- Carl Sagan